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\centerline{MATH 243 -- Mathematical Structures}
\centerline{Quiz 1 -- September 8, 2017}
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\noindent
Your Name: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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\noindent
{\it Directions}
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Do all work and answer all questions on this sheet.  There are 30 possible points, 
distributed as indicated.
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\begin{enumerate}
\item[A)]  Consider this statement about integer $m,n$:  ``If $m\cdot n$ is even, then $m$ is even or $n$ is even.''
\begin{enumerate}
\item[(1)]  (5) Give the \emph{contrapositive} of this statement (any correct form is OK).  
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\item[(2)]  (5) Give the \emph{converse} of this statement.
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\end{enumerate}  
\item[B)]  (10) Give the negation of this statement ``For every real number $x$, there exists a real
number $y$ such that $x \cdot y = 1$.''  Is the statement or its negation true?
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\item[C)] (10) Construct the truth table for the statement ``($P$ and ($P$ implies $Q$)) implies $Q$''
(related to the \emph{modus ponens} inference in classical logic).  
\end{enumerate}
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